A Widom like formula for some Toeplitz plus Hankel determinants

A well known Widom formula expresses the determinant of a Toeplitz matrix Tn with Laurant polynomial symbol f in terms of the zeros of f. We give similar formulae for some even Toeplitz plus Hankel matrices. The formulae are based on an analytic representation of the determinant of such matrices in terms of Chebyshev polynomials.